Certified Energy Auditor Practice Exam

The correct approach to measuring the height of a tree using a stick involves understanding the principles of similar triangles. The method relies on the proportion between the height of the object being measured (the tree) and the height of the stick when held at a certain distance.

When you hold a stick vertically and step back until the top of the stick appears to align with the top of the tree, you create a situation where two triangles are formed: one triangle is between the height of the tree and the distance from the tree, and another triangle is formed by the stick and the distance from the stick's base. Thus, the relation that describes this scenario employs the concept that the ratios of the corresponding sides of similar triangles are equal.

In the formula provided, the height of the tree (H) can be computed by multiplying the height of the stick (h) by the distance to the tree (S) divided by the distance from the base of the stick (s). This proportionality is represented mathematically as H = S * (h/s).

This formula effectively reflects the relationship between the heights and the distances involved, demonstrating how similar triangles can be utilized to find an unknown height based on observable measurements.